pyblp.ProblemResults.run_lm_test

ProblemResults.run_lm_test()

Test the validity of model restrictions with the Lagrange multiplier test.

Following Newey and West (1987), the Lagrange multiplier or score statistic is

(1)\[\text{LM} = N\bar{g}(\hat{\theta})'W\bar{G}(\hat{\theta})V\bar{G}(\hat{\theta})'W\bar{g}(\hat{\theta})\]

where \(\bar{g}(\hat{\theta})\) is defined in (11), \(\bar{G}(\hat{\theta})\) is defined in (19), \(W\) is the optimal weighting matrix in (24), and \(V\) is the covariance matrix of \(\sqrt{N}(\hat{\theta} - \theta)\) in (30).

If the restrictions in this model are valid, the Lagrange multiplier statistic is asymptotically \(\chi^2\) with degrees of freedom equal to the number of restrictions.

Warning

This test requires ProblemResults.W to be an optimal weighting matrix, so it should typically be run only after two-step GMM or after one-step GMM with a pre-specified optimal weighting matrix.

Returns

The Lagrange multiplier statistic.

Return type

float

Examples